Related papers: Lectures on Vertex Operator Algebras and Conformal…

We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by $\mathbb{Z}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a…

Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can…

Conformal algebra is an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality…

An overview of the authors' ideas about the process of completing a $p$-adically normed space in the setting of vertex operator algebras. We focus in particular on the $p$-adic Heisenberg VOA and its connections with $p$-adic modular forms.

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. We review some main convergence results, conjectures and problems in the construction and study of…

We study McKay's observation on the Monster simple group, which relates the 2A-involutions of the Monster simple group to the extended E_8 diagram, using the theory of vertex operator algebras (VOAs). We first consider the sublattices L of…

We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a…

After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…

Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…

For a simple, self-dual, strong CFT-type vertex operator algebra (VOA) of central charge $c$, we describe the Virasoro $n$-point correlation function on a genus $g$ marked Riemann surface in the Schottky uniformisation. We show that this…

In vertex operator algebra theories, most of the general theorems are proved under the assumptions of rationality and C_2-cofiniteness. In this paper, we obtain several general theorems without the assumption of rationality so that we can…

We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible…

A systematic scheme is developed for solving conformal algebra of the massive vertex operators in the old covariant first quantized string theory. Using the first massive level in the covariant spectrum of bosonic open string theory in flat…

This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…

We show that the representation theory for the toroidal extended affine Lie algebras is controlled by a vertex operator algebra which is a tensor product of four VOAs: a sub-VOA of the hyperbolic lattice VOA, two affine VOAs and a Virasoro…

In recent work, Damiolini-Gibney-Tarasca showed that for a $C_2$-cofinite rational CFT-type vertex operator algebra $\mathbb V$, sheaves of conformal blocks are locally free and satisfy the factorization property. In this article, we use…

We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]

We construct a family of vertex algebras associated with a family of symplectic singularity/resolution, called hypertoric varieties. While the hypertoric varieties are constructed by a certain Hamiltonian reduction associated with a torus…

The 3-transposition groups that act on a vertex operator algebra in the way described by Miyamoto are classified under the assumption that the group is centerfree and the VOA carries a positive-definite invariant Hermitian form. This…